Rewrite as a simplified fraction. ${0.9\overline{57} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 957.5757...\\ 10x &= 9.5757...\end{align*}}$ Subtracting the two equations, we have: ${990x = 948}$ ${x = \dfrac{948}{990}} $ ${x = \dfrac{158}{165}} $